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# For one toss of a certain coin, the probability that the out

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Manager
Joined: 16 Feb 2012
Posts: 215
Concentration: Finance, Economics
For one toss of a certain coin, the probability that the out [#permalink]

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09 Jul 2012, 06:50
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54% (01:37) correct 46% (01:38) wrong based on 311 sessions

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For one toss of a certain coin, the probability that the outcome is heads is 0.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?

A. (0.6)^5
B. 2(0.6)^4
C. 3(0.6)^4
D. 4(0.6)^4(0.4) + (0.6)^5
E. 5(0.6)^4(0.4) + (0.6)^5
[Reveal] Spoiler: OA

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Joined: 02 Sep 2009
Posts: 43381
Re: For one toss of a certain coin, the probability that the out [#permalink]

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09 Jul 2012, 06:57
Expert's post
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Stiv wrote:
For one toss of a certain coin, the probability that the outcome is heads is o.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?

A. (0.6)^5
B. 2(0.6)^4
C. 3(0.6)^4
D. 4(0.6)^4(0.4) + (0.6)^5
E. 5(0.6)^4(0.4) + (0.6)^5

$$P(h)=0.6$$, so $$P(t)=0.4$$. We want to determine the probability of at least 4 heads in 5 tries.

At least 4 heads means 4 or 5. Let's calculate each one:

5 heads: $$P(h=5)=0.6^5$$;

4h and 1t: $$P(h=4)=\frac{5!}{4!}*0.6^4*0.4=5*0.6^4*0.4$$, multiplying by 5 as 4h and 1t may occur in 5 different ways:
hhhht
hhhth
hhthh
hthhh
thhhh

So, $$P(h\geq{4})=0.6^5+5*0.6^4*0.4$$.

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Re: For one toss of a certain coin, the probability that the out [#permalink]

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19 Sep 2014, 19:00
Bunuel wrote:
Stiv wrote:
For one toss of a certain coin, the probability that the outcome is heads is o.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?

A. (0.6)^5
B. 2(0.6)^4
C. 3(0.6)^4
D. 4(0.6)^4(0.4) + (0.6)^5
E. 5(0.6)^4(0.4) + (0.6)^5

$$P(h)=0.6$$, so $$P(t)=0.4$$. We want to determine the probability of at least 4 heads in 5 tries.

At least 4 heads means 4 or 5. Let's calculate each one:

5 heads: $$P(h=5)=0.6^5$$;

4h and 1t: $$P(h=4)=\frac{5!}{4!}*0.6^4*0.4=5*0.6^4*0.4$$, multiplying by 5 as 4h and 1t may occur in 5 different ways:
hhhht
hhhth
hhthh
hthhh
thhhh

So, $$P(h\geq{4})=0.6^5+5*0.6^4*0.4$$.

Hi Bunuel,

Thanks for the explanation. I am having difficulty understanding though when should we consider order to be important and when not? When it is not explicitly stated that is..
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Math Expert
Joined: 02 Sep 2009
Posts: 43381
Re: For one toss of a certain coin, the probability that the out [#permalink]

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20 Sep 2014, 12:22
kpali wrote:
Bunuel wrote:
Stiv wrote:
For one toss of a certain coin, the probability that the outcome is heads is o.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?

A. (0.6)^5
B. 2(0.6)^4
C. 3(0.6)^4
D. 4(0.6)^4(0.4) + (0.6)^5
E. 5(0.6)^4(0.4) + (0.6)^5

$$P(h)=0.6$$, so $$P(t)=0.4$$. We want to determine the probability of at least 4 heads in 5 tries.

At least 4 heads means 4 or 5. Let's calculate each one:

5 heads: $$P(h=5)=0.6^5$$;

4h and 1t: $$P(h=4)=\frac{5!}{4!}*0.6^4*0.4=5*0.6^4*0.4$$, multiplying by 5 as 4h and 1t may occur in 5 different ways:
hhhht
hhhth
hhthh
hthhh
thhhh

So, $$P(h\geq{4})=0.6^5+5*0.6^4*0.4$$.

Hi Bunuel,

Thanks for the explanation. I am having difficulty understanding though when should we consider order to be important and when not? When it is not explicitly stated that is..

Think logically, the case of 4 heads and 1 tail can occur in several ways (each of which having the same probability), so we have to account for the order here.
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Re: For one toss of a certain coin, the probability that the out [#permalink]

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12 Sep 2016, 13:53
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For one toss of a certain coin, the probability that the out [#permalink]

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31 May 2017, 22:17
1
KUDOS
Expert's post
Stiv wrote:
For one toss of a certain coin, the probability that the outcome is heads is 0.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?

A. (0.6)^5
B. 2(0.6)^4
C. 3(0.6)^4
D. 4(0.6)^4(0.4) + (0.6)^5
E. 5(0.6)^4(0.4) + (0.6)^5

1. Probability of getting 4 heads and one tail is 5(0.6)^4 * (0.4). 5 is nothing but 5C4 ways. of 4 heads happening.
2. Probability of getting heads all the 5 times is (0.6)^5
3. Total probability is answer E.
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Re: For one toss of a certain coin, the probability that the out [#permalink]

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25 Jun 2017, 11:29
1
KUDOS
Stiv wrote:
For one toss of a certain coin, the probability that the outcome is heads is 0.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?

A. (0.6)^5
B. 2(0.6)^4
C. 3(0.6)^4
D. 4(0.6)^4(0.4) + (0.6)^5
E. 5(0.6)^4(0.4) + (0.6)^5

Refer to the solution in the picture
Attachments

Solution Head.jpeg [ 48.14 KiB | Viewed 973 times ]

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Re: For one toss of a certain coin, the probability that the out [#permalink]

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08 Aug 2017, 06:46
mihir0710 wrote:
Stiv wrote:
For one toss of a certain coin, the probability that the outcome is heads is 0.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?

A. (0.6)^5
B. 2(0.6)^4
C. 3(0.6)^4
D. 4(0.6)^4(0.4) + (0.6)^5
E. 5(0.6)^4(0.4) + (0.6)^5

Refer to the solution in the picture

Thanks for the lucid explanation..
In GMAT can we expect problems related to Bayes’ theorem?
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Re: For one toss of a certain coin, the probability that the out   [#permalink] 08 Aug 2017, 06:46
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